What can industrial inspection models learn from medical analogues? Determining the optimum screening policy for breast cancer

A mathematical model of tumour origination and growth, screening sensitivity, timing of presentation with cancer, and subsequent survival was developed. It was fitted to data for 413 women who screened positive for breast cancer, and for 761 women who developed interval cancers after screening, using the method of maximum likelihood. It was used to find the optimum screening policy, using a simple cost criterion. The model can be classified as a sophisticated ‘delay time’ model, suitable for modelling industrial maintenance data in situations where the size of a defect that can lead to failure is recorded at inspection. Some advantages and disadvantages of this type of model formulation and method of parameter estimation are discussed. A number of statistical and numerical difficulties arise in fitting such complex models, and have as yet no fully satisfactory solution. Industrial modellers must face such problems as data quality improves and more complex models are fitted. The medical screening situation is compared and contrasted with the industrial maintenance situation.